Data-driven Rank Breaking for Efficient Rank Aggregation

Ashish Khetan, Sewoong Oh; 17(193):1−54, 2016.

Abstract

Rank aggregation systems collect ordinal preferences from
individuals to produce a global ranking that represents the
social preference. Rank-breaking is a common practice to reduce
the computational complexity of learning the global ranking. The
individual preferences are broken into pairwise comparisons and
applied to efficient algorithms tailored for independent paired
comparisons. However, due to the ignored dependencies in the
data, naive rank-breaking approaches can result in inconsistent
estimates. The key idea to produce accurate and consistent
estimates is to treat the pairwise comparisons unequally,
depending on the topology of the collected data. In this paper,
we provide the optimal rank-breaking estimator, which not only
achieves consistency but also achieves the best error bound.
This allows us to characterize the fundamental tradeoff between
accuracy and complexity. Further, the analysis identifies how
the accuracy depends on the spectral gap of a corresponding
comparison graph.